Unified Mechanical Analysis Model of the Minimum Substructure for Progressive Collapse Considering Axial Force and Restraint Effects

This study investigated the progressive collapse behavior of steel frame–composite structures based on the finite-element method (FEM), theoretical method, and numerical method, and proposed the theoretical calculation models. First, an overall structural model was analyzed using the alternative path method under various column failure scenarios to examine the structural collapse response and characteristics. The study identified that the area of direct collapse effect (ADCE) was the key mechanical unit controlling the progressive collapse of the structure. By integrating the ADCE under three different failure scenarios and considering different boundary conditions, a unified mechanical analysis model for the minimum substructure was developed, referred to as the “Minimum Substructure Model (MSM).” The MSM can be used to evaluate the collapse resistance of ADCE and predict collapse behavior. The derivation process and calculation method for the full-process collapse response of the MSM were provided. The restraint effects of surrounding structures on the ADCE were emphasized and investigated. The influence of the axial force on the restraint effect was also analyzed. The effects of the axial force and constraint on the MSM model were investigated. For the calculation method of axial force and restraint effects in the MSM, accuracy verification and parameter analysis were conducted at the component, substructure, and overall structure levels. The analysis was progressively conducted to adapt to various usage scenarios. The results show that the theoretical calculation method proposed in this study could accurately determine the restraint effects of surrounding structures on the MSM, with errors less than 10%. At the component level, the axial force weakened the lateral restraint effect of the columns. At the substructure level, the axial force only affected the large deformation stage (LDS) and weakened the ultimate resistance during the LDS. Ignoring the restraint effects tended to overestimate the collapse resistance of the structure, which was on the unconservative side. At the overall structure level, the restraint stiffness gradually decreased with the increase in floor level, with the restraint stiffness of the top floor being over 50% smaller than that of the bottom floor.